Question: Simplify the following expression: $\dfrac{15k}{55k^2}$ You can assume $k \neq 0$.
Explanation: $ \dfrac{15k}{55k^2} = \dfrac{15}{55} \cdot \dfrac{k}{k^2} $ To simplify $\frac{15}{55}$ , find the greatest common factor (GCD) of $15$ and $55$ $15 = 3 \cdot 5$ $55 = 5 \cdot 11$ $ \mbox{GCD}(15, 55) = 5 $ $ \dfrac{15}{55} \cdot \dfrac{k}{k^2} = \dfrac{5 \cdot 3}{5 \cdot 11} \cdot \dfrac{k}{k^2} $ $\phantom{ \dfrac{15}{55} \cdot \dfrac{1}{2}} = \dfrac{3}{11} \cdot \dfrac{k}{k^2} $ $ \dfrac{k}{k^2} = \dfrac{k}{k \cdot k} = \dfrac{1}{k} $ $ \dfrac{3}{11} \cdot \dfrac{1}{k} = \dfrac{3}{11k} $